sinx+sinxcot^2x=cscx

Question

prove each identity

Answer 1

sinx + sinxcot^2x = sinx (1 + cot^2x)
= sinx*(sin^2+cos^2)/sin^2
= 1/sinx
= csc x

Answer 2

LS = sinx(1 + cot^2x)
= sinx(csc^2x)
= sinx(1/sin^2x)
= 1/sinx
= cscx
= RS